Interestingly, it has been proved in [1]} that, in
spherically symmetric hairy black-hole spacetimes, the radius
\(r_{\gamma }\)  of the innermost null circular geodesic sets a lower
bound on the effective length of the external non-linear matter
fields. In particular, it has been proved that in curved black-hole spacetimes that possess hair,
the effective radius of the hair is bounded from below by the compact relation
\(r_{\text{hair}}\ge r_{\gamma }\)  [1]}.
